Abstract

Computational dispersion properties of centered-difference schemes, in terms of frequency and group velocity components, are examined for an anelastic system using a variety of candidates for practically meaningful staggered 3D grids. The numerical analysis is done for dry nonhydrostatic inviscid gravity–inertia wave equations in a Boussinesq system, linearized about a statically stable resting base state with and without Coriolis force. The most advantageous 3D grids are obtained by combining the best horizontal grids, such as the Eliassen and Arakawa C grids, with the best vertical grids, such as the Lorenz and Charney–Phillips grids, and their time-staggemd versions. These best staggered 3D grids provide twice the effective spatial resolution of the regular (unstaggered) 3D grid. The obtained results provide practical guidance for the optimal choice of a grid for anelasfic mesoscale atmospheric models.

Abstract

A new diabatic dynamic initialization technique using an iterative time filter has been developed for an intermittent global data assimilation system. The diabatic dynamic initialization procedure has been implemented within the Goddard Earth Observing System (GEOS) Data Assimilation System employing the GEOS General Circulation Model. The initialization method employs only the forward full diabatic model integration as the initial balancing procedure. The initial balancing is accomplished efficiently by using a new iterative Euler scheme as a filter. The iterative Euler scheme converges rapidly after only a few iterations. It provides a filter most effective for the high-frequency and small-scale modes. The initial spinup effect is almost entirely eliminated, and initially disturbed external and internal modes are balanced by the initialization procedure during the first few time steps. After the short initialization procedure is completed, the standard model integration is continued with the resulting initialized fields, which are now free of noise and spinup effects. Using the new initialization technique, monthly mean analysis and diagnostic fields have been calculated for January and February 1989. The results obtained show the positive impact of the initialization procedure. In particular, the Hadley circulation has been improved.

Most importantly, the global rms height and wind errors calculated against the radiosonde data at station locations are significantly reduced. A set of five comparative 10-day forecasts calculated from initialized and uninitialized analyses show that the scores are moderately to marginally better for the initialized cases.

The initialization procedure is computationally efficient and can be easily applied to various large-scale and mesoscale models/systems.

Abstract

The computational dispersion properties of vertically and time-vertically staggered grids, using corresponding centered-difference schemes for approximation of a linear baroclinic primitive equation system, are analyzed in terms of frequency and group velocity characteristics. The vertical scale ranges with group velocities of the wrong sign are pointed out.

It is shown that among all possible vertical grids applicable to primitive equation atmospheric models the best vertical grids have computational dispersion properties corresponding to a regular (equidistant, unstaggered) grid with twice the vertical resolution. These best vertical grids are 1) two well-known vertically staggered grids, namely, the widely used Lorenz grid and the Charney-Phillips grid; 2) two other vertically staggered grids carrying both horizontal and vertical velocity components at the same levels; and 3) the new time-staggered versions of all the aforementioned grids, and the time-staggered regular vertical grid, if used with either the appropriate version of an economical explicit scheme or a semi-implicit scheme for approximations with these time-staggered grids. All these best vertical grids are computationally efficient due to their enhanced effective vertical resolution.

Moreover, the time-vertically staggered grids considered here provide twice the effective vertical resolution of comparable vertically staggered grids for finite-difference approximations of the vertical derivatives in vertical advection and vertical diffusion terms. In other words, these time-vertically staggered grids provide uniformly twice the elective vertical resolution for the whole baroclinic model system.

The application of higher- (fourth) order vertical-difference approximation results in some moderate improvement of vertical grid dispersion properties, primarily for the small vertical and large horizontal scale range, but it is definitely less significant than the effect of doubling the effective vertical resolution by staggering.

Computational dispersion properties of vertical grids, along with other computational characteristics and requirements, may provide guidance for an optimal choice of an appropriate vertical grid for a primitive equation atmospheric model.

Abstract

The computational dispersion properties of horizontally and time-horizontally staggered grids using corresponding centered-difference schemes for approximation of the Adjustment, or gravity wave equation, are analyzed in terms of their group velocity characteristics. Results are obtained for atmospheric and oceanic models, the latter being characterized by a much smaller Rossby radius of deformation. Three best time-horizontally staggered grids have practically the same advantageous computational dispersion properties as the Arakawa C grid for both atmospheric and oceanic models—namely, the time-staggered D (or Eliassen) and time-staggered C (only with a semi-implicit scheme) grids—and to a certain extent the Lilly grid. Both, the Arakawa B and the time-staggered A grids for atmospheric and oceanic models, along with the Arakawa E and the time-staggered E grids only for atmospheric models (although having worse dispersion properties) also may be used as additional practical options. For all grids considered some additional filtering is needed to control and even eliminate waves with poor computational dispersion characteristics.

Note that along with the B grid widely used in ocean models, the Arakawa C grid, the time-staggered A grid, and especially the time-staggered D (or Eliassen) and C (only with a semi-implicit scheme) grids can be recommended for practical use. The two latter grids have the best dispersion characteristics for ocean models among all staggered grids considered.

Due to the staggering procedure, the grids have enhanced effective resolution that corresponds to the regular Arakawa A grid with half horizontal intervals. Approximate comparative estimates of computation time requirements for different staggered grids versus that of a regular grid are presented for advection and adjustment terms.

Computational dispersion properties along with other computational characteristics and requirements provide some guidance for an optimal choice of an appropriate grid for an atmospheric or ocean model.

Abstract

Simple physical relations (namely, the Rossby ratio between vertical and horizontal scales in quasi-geostrophic flow and the dispersion relation for internal gravity waves) are used to estimate the vertical resolution consistent with a given horizontal resolution. Using these relations we find that virtually all large scale models and observing systems have inadequate vertical resolutions In models, the excess horizontal resolution can lead to increased model “noise” rather than improved accuracy. In observing systems, the finer horizontal scales can be severely misrepresented.

Abstract

A generalized dynamical adjustment procedure has been applied to a diabatic model to produce balanced initial conditions. Namely, backward adiabatic model integration is followed by forward diabatic model integration, with a high-frequency (low-pass) filter in the form of the Euler backward time-differencing scheme being applied throughout the whole integration.

As a result of the application of such a diabatic dynamic initialization procedure within the Goddard Laboratory for Atmospheres (GLA) 4D data-assimilation system, the following properties of forecasts from initialized fields are achieved right from the beginning of the usual forecast integration: 1) the forecast tendencies (and fields) are free of any noise due to imbalance in initial conditions, and 2) the shocks related to an initial imbalance between model physics and dynamics (and especially the substantial initial imbalance of precipitation and evaporation fields), or the initial spinup effect, are practically removed.

Diabatic dynamic initialization has been compared with implicit nonlinear normal-mode initialization and found to be superior in removing the initial spinup effect and in improving the tropical structure.

The diabatic dynamic initialization procedure has been successfully tested for the GLA system with the use of all conventional data and the GLA satellite data retrievals. It allows a smooth data insertion without any shocks or imbalances, which is highly desirable for efficient functioning of 4D data-assimilation systems.

The developed initialization procedure is computationally efficient and in principle easily applicable to different large-scale and mesoscale forecast models.

Abstract

Simple numerical experiments are performed in order to determine the effects of inconsistent combinations of horizontal and vertical resolution in both atmospheric models and observing systems. In both cases, we find that inconsistent spatial resolution is associated with enhanced noise generation.

A rather fine horizontal resolution in a satellite-data observing system seems to be excessive when combined with the usually available relatively coarse vertical resolution. Using horizontal filters of different strengths, adjusted in such a way as to render the effective horizontal resolution more consistent with vertical resolution for the observing system, may result in improvement of the analysis accuracy. The increase of vertical resolution for a satellite-data observing system is, however, desirable. For the conventional-data observing system with better vertically resolved data, the results are different in that little or no horizontal filtering is needed to make spatial resolution more consistent for the system.

The obtained experimental estimates of consistent vertical and effective horizontal resolution are in a general agreement with consistent resolution estimates previously derived theoreticdly by the authors.

Abstract

The onset and evolution of the North American monsoon system during the summer of 1993 were examined from regional to large scales using the National Aeronautics and Space Administration (NASA) Goddard Earth Observing System (GEOS) stretched-grid GCM. The model's grid spacing for the dynamical core ranges from 0.4° × 0.5° in latitude–longitude over the United States to about 2.5° × 3.5° at the antipode, and the physical package is solved on an intermediate 1° × 1° uniform grid. A diagnostic analysis of the monsoon's onset reveals the development of a positive potential temperature (θ) anomaly at the surface that favors a lower-level cyclonic circulation, while a negative potential vorticity (PV) anomaly below the tropopause induces an upper-level anticyclonic circulation. Ignoring diabatic effects, this pattern is consistent with the superimposition of idealized PV and θ anomalies as previously discussed in the literature. The inclusion of the smaller-scale features of the core monsoon in the model simulation helps represent the continental out-of-phase relationship between the monsoon and the southern Great Plains precipitation, giving additional support to earlier results that highlight the strong nature of the link. A pattern of increased precipitation over the core monsoon is consistently associated with increases of moisture flux convergence and ascending motions, and the development of upper-level wind divergence. On the other hand, the southern Great Plains have a simultaneous decrease of precipitation associated with a change from convergence to divergence of moisture flux, decreased ascending motions, and a development of upper-level wind convergence.

The Gulf of California low-level jet (LLJ) was inspected with a multitaper method spectral analysis, showing significant peaks for both the diurnal cycle and synoptic-scale modes, the latter resulting from the recurrent passage of Gulf surges. Those modes were then separated with a singular spectrum analysis decomposition. Compared with the Great Plains LLJ, the Gulf of California LLJ has a weaker diurnal cycle amplitude and a smaller ratio of diurnal cycle to synoptic-scale amplitudes. Additionally, the 1993 southwestern U.S. monsoon was analyzed by constructing composites of surge and no-surge cases. Given the particular characteristics of 1993 that include the effect of Hurricane Hilary, the extension of these results to other years needs to be assessed. Surges are associated with a strong Gulf of California LLJ and increased moisture flux from the Gulf into Arizona, and they accounted for 80%–100% of the simulated precipitation over Arizona, western New Mexico, and southern Utah. As distance from the Gulf is increased, there is a rapid decay of this percentage so that northern Utah and eastern New Mexico precipitation is almost unrelated to the surges. The results from this research show that the model's regional downscaling results in a realistic representation of the monsoon-related circulations at multiple scales.

Abstract

An approach to calculating model physics using neural network emulations, previously proposed and developed by the authors, has been implemented in this study for both longwave and shortwave radiation parameterizations, or to the full model radiation, the most time-consuming component of model physics. The developed highly accurate neural network emulations of the NCAR Community Atmospheric Model (CAM) longwave and shortwave radiation parameterizations are 150 and 20 times as fast as the original/control longwave and shortwave radiation parameterizations, respectively. The full neural network model radiation was used for a decadal climate model simulation with the NCAR CAM. A detailed comparison of parallel decadal climate simulations performed with the original NCAR model radiation parameterizations and with their neural network emulations is presented. Almost identical results have been obtained for the parallel decadal simulations. This opens the opportunity of using efficient neural network emulations for the full model radiation for decadal and longer climate simulations as well as for weather prediction.

Abstract

This reply is aimed at clarifying and further discussing the methodological aspects of this neural network application for a better understanding of the technique by the journal readership. The similarities and differences of two approaches and their areas of application are discussed. These two approaches outline a new interdisciplinary field based on application of neural networks (and probably other modern machine or statistical learning techniques) to significantly speed up calculations of time-consuming components of atmospheric and oceanic numerical models.